泰勒级数

指数函数和自然对数

三角函数

习题中常见

$$\sum _{n=1}^{\infty }n{x}^n=\frac{x}{(x-1{)}^2}$$

Sum of a power series n*xn - Mathematics Stack Exchange

$$\sum _0^{\infty }{n}^2{x}^n=\frac{x(1+x)}{(1-x{)}^3}$$

How can I calculate this infinite sum math {n^2 x^n}math - Quora